Probability distributions from a linear regression model

Question

I've constructed a Linear Regression model (OLS) and I'm wondering what the statistical certainty is for the response variable to be true.

Say I'm collecting data from a biological system and I want to predict the weight of the cells, e.g resulting in y=50mg. I want to figure out how certain I am that y=50mg is true.

Also, if I assume intervall values 1-10mg, 11-20, 21-30.. 91-100mg - can I assume linear distribution i.e that if y=50mg then it's a 10% chance that the values is between 41-50mg (and nothing more) or am I equipped to assume trapezoidal probability function i.e that it's a 50% chance that the value is 41-50mg or less.

Any thoughts on this?

Answer 1

OLS is based on the Normal distribution, which is continuous. If this model predicts a response of 50mg, then what it is really saying is that it expects the response to come from a Normal distribution with mean 50mg and some standard deviation. For the sake of concreteness I'll say that SD is 5mg.

The chance of the response being exactly 50mg is zero under this model. However, what I think you are really asking is "what is the chance the observed value rounds to 50mg (i.e. it's between 49.5 and 50.5, or between 45 and 55). This can be computed by referring to tables or using inbuilt calculator functions. In my example the probability of being between 49.5 and 50.5 would have been a little under 8%, and of being between 45 and 55 would have been 68%.